Hoffman index of manifolds

مقدم أطروحة جامعية

Sadiq, Afra Radi

مشرف أطروحة جامعية

Fathi, Sakin A.

أعضاء اللجنة

Majid, Wasan Khalid
Majid, Abd al-Rahman Hamid
Khidr, Jihad Ramadan
al-Bahrani, Bahar Hamad Ahmad
Mansur, Nadir Jurj

الجامعة

جامعة بغداد

الكلية

كلية العلوم

القسم الأكاديمي

قسم الرياضيات

دولة الجامعة

العراق

الدرجة العلمية

دكتوراه

تاريخ الدرجة العلمية

2007

الملخص الإنجليزي

Let X be a topological space and f : X ! X be a map, a point x 2 X is called a fixed point for f if f(x) = x and x is a periodic point if there exists k 2 N such that fk(x) = x.

More generally, if f, g : X ! X are maps, then a point x 2 X is a coincidence point for f and g if f(x) = g(x).

The no coincidence index is a topological invariant reflecting the number of fixed-point-free-self maps of a connected topological manifold M such that no pair of these maps has a coincidence.

This concept was introduced and studied by M.

Hoffman in 1984, he gave sufficient conditions for a manifold M, to have no coincidence index #M = 1.

Also he computed the no coincidence index for some important homogenous spaces (the flag manifolds).

In 1989 M.

Hoffman continued his study of this concept and he gave necessary and sufficient conditions for a manifold to have finite no coincidence index.

In this thesis, we study this concept and prove some results that are stated in the literature without proofs.

We also give details of the proofs of many important results, and illustrate these results by some examples.

We give some new results related to this concept.

We define two new indices, the homeomorphism no coincidence index and the period no coincidence index, and give some useful results for computing each of these indices.

Also we give results relating these indices with the no coincidence index of Hoffman.

التخصصات الرئيسية

الرياضيات

الموضوعات

• النماذج الرياضية

عدد الصفحات

134

قائمة المحتويات

• APA
• MLA
• AMA

لغة النص

الإنجليزية

نوع البيانات

رسائل جامعية

رقم السجل

BIM-603137